If an object moves at a non-zero constant acceleration for a certain interval of time, then the distance it covers in that time.

For an object moving with a non-zero constant acceleration, the displacement (s) is governed by the kinematic equation s = ut + ½at², where 'u' is the initial velocity, 'a' is the acceleration, and 't' is the time interval. This equation demonstrates that the distance covered depends on both the initial velocity and the time elapsed. If the initial velocity is non-zero, the term 'ut' contributes significantly to the total distance. While displacement is proportional to the square of time when the initial velocity is zero, a general case with non-zero initial velocity makes the relationship a combination of linear and quadratic terms. Therefore, the distance covered is not independent of the initial velocity, nor does it increase purely linearly with time due to the quadratic acceleration term. Initial displacement only shifts the final position but does not change the distance covered during the interval.